A conventional three-dimensional back projection method will be explained. A Feldkamp method, Wang method, IHCB method and PI-method proposed as three-dimensional back projection methods are three-dimensional back projection methods which capture a cone beam spreading (having an angle of inclination) in both the slice (body axis) direction and channel (rotation) direction irradiated to multi-row radiation detectors as a collection of a plurality of rows of fan beams spreading only in the channel direction, carry out filter correction processing similar to a two-dimensional back projection method on the fan beam projection data obtained from each detector row or parallel beam projection data obtained by replacing the fan beam by parallel beam through rearrangement processing and carry out back projection processing along the trace of the beam to thereby obtain a reconfigured image.
FIG. 7 shows a reconfigurable condition of a Wang method and FIG. 8 shows a reconfigurable condition of a PI-method. Here, reference character FOV denotes an effective field of view region, SOD denotes a distance between an X-ray tube and the go-around axis of a CT device and SID denotes a distance between the X-ray tube and detector. The Wang method is a method corresponding to a Feldkamp method adapted to image taking of a spiral orbit and has a back projection phase width of π to 2π.
An example of a PI-method is disclosed in JP-A-11-253434. This is also a back projection method applicable to image taking of a spiral orbit and is a reconfiguration method for back projecting a π range in which the phase varies from one voxel to another to improve a bed moving speed using the Wang method. The PI-method can set the back projection phase range for each voxel to π by limiting the vertical direction of an X-ray beam to be back projected using a spiral located opposite to the X-ray focal position.
An example of the IHCB method is disclosed in JP-A-11-4823. This method consists of an algorithm for back projecting a back projection phase range which varies from one voxel to another and the back projection phase width is either π or an entire possible data range which varies from one voxel to another.
Next, problems of these conventional technologies will be explained.
The Feldkamp method is an image reconfiguration method for image taking of a circular orbit and is not applicable to image taking of a spiral orbit. The Wang method is an image reconfiguration method for image taking of a spiral orbit and can correct influences of movement of an examinee, which is practiced by the conventional two-dimensional back projection method by extending the back projection phase width beyond π (increasing data redundancy), but results in a poor data utilization rate and the pitch (hereinafter referred to as “measuring throughput”) of the spiral during image taking needs to be very small. By improving the PI-method and IHCB method so that the back projection phase range according to the Wang method is widened, their respective measuring throughputs can be drastically improved compared to the Wang method, but they are the back projection methods within the π range with data redundancy completely eliminated, and therefore data may be discontinuous at the start phase and end phase of the back projection phase range due to influences of movement of the examinee, which is likely to become a strong artifact and appear on the image.
Here, data redundancy will be explained. The data redundancy refers to a breadth of a phase range within which not only phase data but also opposed phase data is acquired. According to a three-dimensional back projection method, data redundancy changes from one voxel to another. For example, as shown in FIG. 22, when back projection is performed from data obtained by rotating the phase of a radiation source by 180 degrees, the contributing data phase range changes from one reconfiguration pixel to another and a pixel a has data having a phase range of 180 degrees or more, while a pixel b can only acquire data of 180 degrees or less. Furthermore, it is also necessary to consider the beam width in the body axis direction and in this way data redundancy changes from one pixel to another in a complicated manner. For this reason, a complicated redundancy correction is required.
One of problems of these conventional three-dimensional reconfigurations is an increase in a calculation time.
Therefore, when an increase in the amount of calculation from a parallel beam two-dimensional back projection method to a parallel beam three-dimensional back projection method is analyzed, the increased calculation causes (1) an increase in the number of times one-dimensional rearrangement processing is performed, (2) an increase in the number of times reconfiguration filter processing is performed and (3) an addition of calculation of detector row addresses during back projection processing. Here, the main processing that occupies the calculation time in the two-dimensional back projection method and three-dimensional back projection method is back projection processing.
The loads of calculation of the distance between the focus and reconfiguration point during the calculation of detector row addresses and arcsin calculation (calculation of the z position of the focus of the parallel beam of the following Expression 1) are particularly large and occupy the major portion of causes of increases in the calculation time.zS=(J·(φ+arcsin(tI/SOD))/2π)+zSO  [Expression 1]
See FIG. 29.
Suppose SOD is a distance between a radiation source and a go-around axis, φ is a phase angle of the parallel beam, J is a relative movement distance from a radiation source to an examinee per rotation of a scanner on a radiation detector 13, tI is the position in the channel direction, zs is the position of the radiation source 11 in the z direction and zs0 is zs when the go-around phase of the radiation source is 0. Therefore, if these calculations can be simplified, it is possible to significantly increase the processing speed of the tomograph.
It is an object of the present invention to provide a tomograph capable of suppressing generation of the distortion attributed to data discontinuity and obtaining a tomographic image of high image quality not eliminating data redundancy but rather using it in three-dimensional back projection calculations.
It is another object of the present invention to provide a tomograph capable of simplifying arcsin calculation on a fan-parallel beam conversion and back projection processing according to a set FOV range in three-dimensional back projection calculations and significantly increasing the processing speed of the tomograph without degrading image quality.